Speeding up compact planar graphs by using shallower trees

A common technique to design compact representations for planar graphs is to decompose the graph into spanning trees, which are later represented compactly. In some representations of planar graphs, such as Turan's representation, the topology of such spanning trees is not fixed. In this work, we show that the topology of the spanning trees used in the representation impacts the performance of typical operations of compact planar graphs. Hence, by computing suitable spanning trees and improving their compact representation, we provide compact representations of planar graphs that are both smaller and faster than the state of the art.